IJPAM: Volume 108, No. 4 (2016)

NUMERICAL SOLUTION FOR VARIABLE-ORDER
LINEAR CABLE EQUATIONS WITH SHIFTED
SECOND KIND CHEBYSHEV POLYNOMIALS

Leili Masoudi$^1$, M. Tavassoli Kajani$^2$ $^{1,2}$Department of Mathematics
Isfahan (Khorasgan) Branch
Islamic Azad University
Isfahan, IRAN


Abstract. In this paper, we apply second kind Chebyshev polynomials to solve variable-order linear cable equations. First, we convert second kind Chebyshev polynomials on the interval $[-1,1]$ into $[0,R]$. Then we reduce variable-order linear cable equation to a set of algebraic equations by using second kind shifted Chebyshev polynomials and collocation method. To obtain an approximate solution of the linear cable equation, we should solve this algebraic system. The results demonstrate that the proposed method has high accuracy and effectiveness for solving the variable-order linear cable equations. The validity and effectiveness of the method are demonstrated by solving several numerical examples.

Received: April 11, 2016

AMS Subject Classification:

Key Words and Phrases: variable-order linear cable equations, fractional PDE, Chebyshev polynomials, collocation method

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DOI: 10.12732/ijpam.v108i4.10 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 108
Issue: 4
Pages: 849 - 857


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